The standard form of the circle is:
(x-h)^2+(y-k)^2=r^2, where (h,k) is the center of the circle and r is its radius...
We are given the center is (8,4) so we have:
(x-8)^2+(y-4)^2=r^2
So we now have to find the radius. Since (-9,-7) is on the circle and the center is (8,4), the distance between these two points is equal to the radius...
r^2=(dx)^2+(dy)^2
r^2=(8--9)^2+(4--7)^2
r^2=17^2+11^2
r^2=289+121
r^2=410 so now we have the complete standard equation for this circle:
(x-8)^2+(y-4)^2=410